\name{finterp}
\alias{finterp}
\alias{finterp.default}
\alias{fmobj}

\title{ Formula Interpreter }
\description{ This function is taken from Jim Lindsey's R package \code{rmutil}. 

What follows is taken from the help file of \code{rmutil}. 
Note that not all the functionalities of \code{finterp} are implemented in \code{nlgamlss}. 

  
 \code{finterp} translates a model formula into a function of the
     unknown parameters or of a vector of them. Such language formulae
     can either be in Wilkinson and Rogers notation or be expressions
     containing both known (existing) covariates and unknown (not
     existing) parameters. In the latter, factor variables cannot be
     used and parameters must be scalars.

     The covariates in the formula are sought in the environment or in
     the data object provided. If the data object has class, 'repeated'
     or 'response', then the key words, 'times' will use the response
     times from the data object as a covariate, 'individuals' will use
     the index for individuals as a factor covariate, and 'nesting' the
     index for nesting as a factor covariate. The latter two only work
     for W&R notation.

     Note that, in parameter displays, formulae in Wilkinson and Rogers
     notation use variable names whereas those with unknowns use the
     names of these parameters, as given in the formulae, and that the
     meaning of operators (*, /, :, etc.) is different in the two
     cases.
     
      The function \code{fmobj} inspects a formula and returns a list containing the
     objects referred to, with indicators as to which are unknown
     parameters, covariates, factor variables, and functions.
}
\usage{
finterp.default(.z, .envir = parent.frame(), .formula = FALSE, 
       .vector = TRUE, .args = NULL, .start = 1, 
       .name = NULL, .expand = TRUE, .intercept = TRUE, 
       .old = NULL, .response = FALSE, ...)
finterp(.z, ...)
fmobj(z, envir = parent.frame())
}

\arguments{
 \item{.z}{A model formula beginning with \~, either in Wilkinson and
          Rogers notation or containing unknown parameters. If it
          contains unknown parameters, it can have several lines so
          that, for example, local variables can be assigned temporary
          values. In this case, enclose the formula in curly brackets }
  \item{.envir}{The environment in which the formula is to be interpreted or
          a data object of class, 'repeated', 'tccov', or 'tvcov'. }
  \item{.formula}{ If TRUE and the formula is in Wilkinson and Rogers notation,
          just returns the formula.}
  \item{.vector}{If FALSE and the formula contains unknown parameters, the
          function returned has them as separate arguments. If TRUE, it
          has one argument, the unknowns as a vector, unless certain
          parameter names are specified in '.args'. Always TRUE if
          '.envir' is a data object. }
  \item{.args}{If '.vector' is TRUE, names of parameters that are to be
          function arguments and not included in the vector. }
  \item{.start}{ The starting index value of the parameter vector in the
          function returned when '.vector' is TRUE. }
  \item{.name}{ Character string giving the name of the data object specified
          by '.envir'. Ignored unless the latter is such an object and
          only necessary when 'finterp' is called within other
          functions.}
  \item{.expand}{If TRUE, expand functions with only time-constant covariates
          to return one value per observation instead of one value per
          individual. Ignored unless '.envir' is an object of class,
          'repeated'. }
  \item{.intercept}{If W&R notation is supplied and '.intercept=F', a model
          function without intercept is returned. }
  \item{.old}{The name of an existing object of class 'formulafn' which has
          common parameters with the one being created, or a list of
          such objects. Only used if '.vector'=TRUE. The value of
          '.start' should ensure that there is no conflict in indexing
          the vector. }
  \item{.response}{ If TRUE, any response variable can be used in the function.
          If FALSE, checks are made that the response is not also used
          as a covariate.} 
  \item{z}{A model formula beginning with ~, either in Wilkinson and
          Rogers notation or containing unknown parameters.}
  \item{envir}{The environment in which the formula is to be interpreted.}
   \item{\dots}{for extra arguments}    
}

\value{
  A function, of class \code{formulafn}, of the unknown parameters or of
     a vector of them is returned. Its attributes give the formula
     supplied, the model function produced, the covariate names, the
     parameter names, and the range of values of the index of the
     parameter vector. If 'formula' is TRUE and a Wilkinson and Rogers
     formula was supplied, it is simply returned instead of creating a
     function.
     
     For \code{fmobj} a list, of class 'fmobj', containing a character vector
     ('objects') with the names of the objects used in a formula, and
     logical vectors indicating which are unknown parameters
     ('parameters'), covariates ('covariates'), factor variables
     ('factors'), and functions ('functions') is returned.


}
\references{ \url{http://popgen.unimaas.nl/~jlindsey/index.html: Jim Lindsey web page} }
\author{  J.K. Lindsey }


\examples{
# From Jim Lindsey
x1 <- rpois(20,2)
x2 <- rnorm(20)
#
# Wilkinson and Rogers formula with three parameters
fn1 <- finterp(~x1+x2)
fn1
fn1(rep(2,3))
# the same formula with unknowns
fn2 <- finterp(~b0+b1*x1+b2*x2)
fn2
fn2(rep(2,3))
#
# nonlinear formulae with unknowns
# log link
fn2a <- finterp(~exp(b0+b1*x1+b2*x2))
fn2a
fn2a(rep(0.2,3))
# parameters common to two functions
fn2b <- finterp(~c0+c1*exp(b0+b1*x1+b2*x2), .old=fn2a, .start=4)
fn2b
# function returned also depends on values of another function
fn2c <- finterp(~fn2+c1*exp(b0+b1*x1+b2*x2), .old=fn2a,
        .start=4, .args="fn2")
fn2c
args(fn2c)
fn2c(rep(0.2,4),fn2(rep(2,3)))
#
# compartment model
times <- 1:20
# exp() parameters to ensure that they are positive
fn3 <- finterp(~exp(absorption-volume)/(exp(absorption)-
        exp(elimination))*(exp(-exp(elimination)*times)-
        exp(-exp(absorption)*times)))
fn3
fn3(log(c(0.3,3,0.2)))
# a more efficient way
# (note that parameters do not appear in the same order)
form <- ~{
        ka <- exp(absorption)
        ke <- exp(elimination)
        ka*exp(-volume)/(ka-ke)*(exp(-ke*times)-exp(-ka*times))}
fn3a <- finterp(form)
fn3a(log(c(0.3,0.2,3)))
#
# Poisson density
y <- rpois(20,5)
fn4 <- finterp(~mu^y*exp(-mu)/gamma(y+1))
fn4
fn4(5)
dpois(y,5)
#
# Poisson likelihood
# mean parameter
fn5 <- finterp(~-y*log(mu)+mu+lgamma(y+1),.vector=FALSE)
fn5
likefn1 <- function(p) sum(fn5(mu=p))
nlm(likefn1,p=1)
mean(y)
# canonical parameter
fn5a <- finterp(~-y*theta+exp(theta)+lgamma(y+1),.vector=FALSE)
fn5a
likefn1a <- function(p) sum(fn5a(theta=p))
nlm(likefn1a,p=1)
#
# likelihood for Poisson log linear regression
y <- rpois(20,fn2a(c(0.2,1,0.4)))
nlm(likefn1,p=1)
mean(y)
likefn2 <- function(p) sum(fn5(mu=fn2a(p)))
nlm(likefn2,p=c(1,0,0))
# or
likefn2a <- function(p) sum(fn5a(theta=fn2(p)))
nlm(likefn2a,p=c(1,0,0))
#
# likelihood for Poisson nonlinear regression
y <- rpois(20,fn3(log(c(3,0.3,0.2))))
nlm(likefn1,p=1)
mean(y)
likefn3 <- function(p) sum(fn5(mu=fn3(p)))
nlm(likefn3,p=log(c(1,0.4,0.1)))
#
# envir as data objects
# y <- matrix(rnorm(20),ncol=5)
#y[3,3] <- y[2,2] <- NA
#x1 <- 1:4
#x2 <- c("a","b","c","d")
#resp <- restovec(y)
#xx <- tcctomat(x1)
#xx2 <- tcctomat(data.frame(x1,x2))
#z1 <- matrix(rnorm(20),ncol=5)
#z2 <- matrix(rnorm(20),ncol=5)
#z3 <- matrix(rnorm(20),ncol=5)
#zz <- tvctomat(z1)
#zz <- tvctomat(z2,old=zz)
#reps <- rmna(resp, ccov=xx, tvcov=zz)
#reps2 <- rmna(resp, ccov=xx2, tvcov=zz)
#rm(y, x1, x2 , z1, z2)
#
# repeated objects
#
# time-constant covariates
# Wilkinson and Rogers notation
#form1 <- ~x1
#print(fn1 <- finterp(form1, .envir=reps))
#fn1(2:3)
#print(fn1a <- finterp(form1, .envir=xx))
#fn1a(2:3)
#form1b <- ~x1+x2
#print(fn1b <- finterp(form1b, .envir=reps2))
#fn1b(2:6)
#print(fn1c <- finterp(form1b, .envir=xx2))
#fn1c(2:6)
# with unknown parameters
#form2 <- ~a+b*x1
#print(fn2 <- finterp(form2, .envir=reps))
#fn2(2:3)
#print(fn2a <- finterp(form2, .envir=xx))
#fn2a(2:3)
#
# time-varying covariates
# Wilkinson and Rogers notation
#form3 <- ~z1+z2
#print(fn3 <- finterp(form3, .envir=reps))
#fn3(2:4)
#print(fn3a <- finterp(form3, .envir=zz))
#fn3a(2:4)
# with unknown parameters
#form4 <- ~a+b*z1+c*z2
#print(fn4 <- finterp(form4, .envir=reps))
#fn4(2:4)
#print(fn4a <- finterp(form4, .envir=zz))
#fn4a(2:4)
#
# note: lengths of x1 and z2 differ
# Wilkinson and Rogers notation
#form5 <- ~x1+z2                
#print(fn5 <- finterp(form5, .envir=reps))
#fn5(2:4)
# with unknown parameters
#form6 <- ~a+b*x1+c*z2
#print(fn6 <- finterp(form6, .envir=reps))
#fn6(2:4)
#
# with times
# Wilkinson and Rogers notation
#form7 <- ~x1+z2+times
#print(fn7 <- finterp(form7, .envir=reps))
#fn7(2:5)
#form7a <- ~x1+x2+z2+times
#print(fn7a <- finterp(form7a, .envir=reps2))
#fn7a(2:8)
# with unknown parameters
#form8 <- ~a+b*x1+c*z2+e*times
#print(fn8 <- finterp(form8, .envir=reps))
#fn8(2:5)
#
# with a variable not in the data object
#form9 <- ~a+b*z1+c*z2+e*z3
#print(fn9 <- finterp(form9, .envir=reps))
#fn9(2:5)
# z3 assumed to be an unknown parameter:
#fn9(2:6)
#
# multiline formula
#form10 <- ~{
#        tmp <- exp(b)
#        a+tmp*z1+c*z2+d*times}
#print(fn10 <- finterp(form10, .envir=reps))
#fn10(2:5)
# for fmobj
 x1 <- rpois(20,2)
 x2 <- rnorm(20)
 x3 <- gl(2,10)
 #
 # W&R formula
 fmobj(~x1+x2+x3)
 #
 # formula with unknowns
 fmobj(~b0+b1*x1+b2*x2)
 #
 # nonlinear formulae with unknowns
 # log link
 fmobj(~exp(b0+b1*x1+b2*x2))
}
\keyword{regression}% at least one, from doc/KEYWORDS
